Illegal immigrant soldiers?

Other than what part of "illegal" people (including President Barack Obama) don't understand, what I find incredibly and utterly unbelievable regarding President Obama's exemption for illegal immigrants having served in the military is this: How is it that illegal immigrants are allowed to join our military in the first place? Could somebody please explain?

If theU.S. Department of Defensecan't keep illegal immigrants out of its own service branches, we might as well do away with all border controls, eliminate any requirements for entry to this country and throw open our borders to anyone and everyone who wants to come here.